Am I Blue? Finding the Right (Spectral) Balance

Seismic interpreters have always desired to extract as much vertical resolution from their data as possible – and that desire has only increased with the need to accurately land horizontal wells within target lithologies that fall at or below the limits of seismic resolution.

Although we often think of increasing the higher frequencies, resolution should be measured in the number of octaves, whereby halving the lowest frequency measured doubles the resolution.

There are several reasons why seismic data are band-limited.

First, if a vibrator sweep ranges between 8 and 120 Hz, the only “signal” outside of this range is in difficult to process (and usually undesirable) harmonics.

Dynamite and airgun sources may have higher frequencies, but conversion of elastic to heat energy (intrinsic attenuation), scattering from rugose surfaces and thin bed reverberations (geometric attenuation) attenuate the higher frequency signal to a level where they fall below the noise threshold. Geophone and source arrays attenuate short wavelength events where individual array elements experience different statics. Processing also attenuates frequencies. Processors often need to filter out the lowest frequencies to attenuate ground roll and ocean swell noise. Small errors in statics and velocities result in misaligned traces that when stacked preserve the lower frequencies but attenuate the higher frequencies.


Currently there are two approaches to spectral enhancement.

More modern innovations that have been given names such as “bandwidth extension,” “spectral broadening” and “spectral enhancement,” are based on a model similar to deconvolution, which assumes the earth is composed of discrete, piecewise constant impedance layers. Such a “sparse spike” assumption allows one to replace a wavelet with a spike, which is then replaced with a broader band wavelet that often exceeds the bandwidth of the seismic source.

Model-based processing is common to reflection seismology and often provides excellent results – however, the legitimacy of the model needs to be validated, such as tying the broader band product to a well not used in the processing workflow.

We have found bandwidth extension algorithms to work well in lithified Paleozoic shale resource plays and carbonate reservoirs.

In contrast, bandwidth extension can work poorly in Tertiary Basins where the reflectivity sequence is not sparse, but rather represented by upward fining and coarsening patterns.

In this article, we review the more classical workflow of spectral balancing, constrained to fall within the source bandwidth of the data.

Spectral balancing was introduced early in digital processing during the 1970s and is now relatively common in the workstation environment.


As summarized in figure 1, the interpreter decomposes each seismic trace into a suite of 5-10 overlapping pass band filtered copies of the data. Each band-passed filtered version of the trace is then scaled such that the energy within a long (e.g. 1,000 ms) window is similar down the trace.

This latter process is called automatic gain control, or AGC.

Once all the components are scaled to the same target value they are then added back together, providing a spectrally balanced output.

A more recent innovation introduced about 10 years ago is to add “bluing” to the output. In this latter case, one stretches the well logs to time, generates the reflectivity sequence from the sonic and density log and then computes its spectrum. Statistically, such spectra are rarely “white,” with the same values at 10 Hz and 100 Hz, but rather “blue,” with larger magnitude spectral components at higher (bluer) frequencies than at lower (redder) frequencies.

The objective in spectrally balancing then is to modify the seismic trace spectrum so that it approximates the well log reflectivity spectrum within the measured seismic bandwidth.

Such balancing is achieved by simply multiply each band-pass filtered and AGC’d component by exp(+βf), where f is the center frequency of the filter and β is the parameter that is obtained from the well logs that varies between 0.0 and 0.5 (black boxes in figure 1).

There are several limitations to this classic workflow:

First, one balances the measured seismic data, which is the sum of the signal plus noise. Ideally, we want to balance the signal.

Second, since the filters are applied trace by trace, the process as a whole is not amplitude friendly and inappropriate as input to more quantitative amplitude-sensitive analysis such as AVO and post-stack or prestack inversion.

Third, if the AGC window is too small or the statistics of the reflectivity sequence insufficiently smooth (an end member example would be coal bed cyclothems and sabkha sequencies), then reflectors of interest can be suppressed and artifacts created.

A fairly common means of estimating the spectrum of the signal is to cross-correlate adjacent traces to differentiate that part of the signal that is consistent (signal) and that part that is inconsistent (random noise). One then designs the spectral balancing parameters (AGC coefficients) on the consistent part of the data.

Unfortunately, this approach is still not amplitude friendly and can remove geology if the spectra are not smooth.


Figure 2 illustrates a more modern approach that can be applied to both post-stack and prestack migrated data volumes.

First, we suppress crosscutting noise using a structure-oriented filtering algorithm, leaving mostly signal in the data.

Next, the data are decomposed into time-frequency spectral components.

Finally, we compute a smoothed average spectrum.

If the survey has sufficient geologic variability within the smoothing window (i.e. no perfect “railroad tracks”), this spectrum will represent the time-varying source wavelet.

This single average spectrum is used to design a single time-varying spectral scaling factor that is applied to each and every trace. Geologic tuning features and amplitudes are thus preserved.

We apply this workflow to a legacy volume acquired in the Gulf of Mexico:

  • Figures 3a and b show the average spectrum before and after spectral balancing.
  • Figures 3c and d show a representative segment of the seismic data where we see the vertical resolution has been enhanced.

 

Comments (0)

 

Geophysical Corner

Geophysical Corner - Satinder Chopra
Satinder Chopra, award-winning chief geophysicist (reservoir), at Arcis Seismic Solutions, Calgary, Canada, and a past AAPG-SEG Joint Distinguished Lecturer began serving as the editor of the Geophysical Corner column in 2012.

Marcílio Matos is a research scientist for Signal Processing Research, Training and Consulting, and co-investigator for the Attribute Assisted Seismic Processing and Interpretation Consortium at the University of Oklahoma, Norman.

Geophysical Corner - Kurt Marfurt
AAPG member Kurt J. Marfurt is with the University of Oklahoma, Norman, Okla.

Geophysical Corner

The Geophysical Corner is a regular column in the EXPLORER that features geophysical case studies, techniques and application to the petroleum industry.

VIEW COLUMN ARCHIVES

Image Gallery

See Also: DL Abstract

Hydrocarbon exploration beneath the shallow allochthonous salt canopy of the ultra-deepwater central Gulf of Mexico has encountered three thick, sand-rich, submarine fan successions that punctuate an otherwise relatively condensed and fine-grained basin center stratigraphy. These sand-rich fans are Late Paleocene, Early Miocene, and Middle Miocene in age and each coincide with periods of very high sediment flux and basin margin instability. They are the primary exploration targets in most ultra-deepwater fields, recent discoveries, and failed exploration tests.

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 3079 DL Abstract

Over the last two decades, numerical and physical experiments have repeatedly generated insights that contradict the sequence stratigraphic model that is near-universally used to interpret ancient strata in terms of relative changes in sea-level. This presentation will re-examine Upper Cretaceous strata (Blackhawk Formation, Castlegate Sandstone, Mancos Shale) exposed in the Book Cliffs, east-central Utah, USA, which are widely used as an archtype for the sequence stratigraphy of marginal-marine and shallow-marine strata. Stratigraphic architectures in these strata are classically interpreted to reflect forcing by relative sea level, but key aspects can instead be attributed to autogenic behaviors and variations in sediment flux.

Desktop /Portals/0/PackFlashItemImages/WebReady/reinterpretation-of-sea-level-driven-stratigraphic-architectures-hero.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 11401 DL Abstract

The Gulf of Mexico (GOM) is the 9th largest body of water on earth, covering an area of approximately 1.6 million km2 with water depths reaching 4,400 m (14,300’). The basin formed as a result of crustal extension during the early Mesozoic breakup of Pangaea. Rifting occurred from the Late Triassic to early Middle Jurassic. Continued extension through the Middle Jurassic combined with counter-clockwise rotation of crustal blocks away from North America produced highly extended continental crust in the subsiding basin center. Subsidence eventually allowed oceanic water to enter from the west leading to thick, widespread, evaporite deposition. Seafloor spreading initiated in the Late Jurassic eventually splitting the evaporite deposits into northern (USA) and southern (Mexican) basins. Recent work suggests that this may have been accomplished by asymmetric extension, crustal delamination, and exposure of the lower crust or upper mantle rather than true sea floor spreading (or it could be some combination of the two). By 135 Ma almost all extension had ceased and the basic configuration of the GOM basin seen today was established. The Laramide Orogeny was the last major tectonic event impacting the GOM. It caused uplift and erosion for the NW margin from the Late Cretaceous to early Eocene.

Desktop /Portals/0/images/_site/AAPG-newlogo-vertical-morepadding.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 3078 DL Abstract

See Also: Energy Policy Blog

18 percent of AAPG members are women, up from 10 percent in 2006.

Desktop /Portals/0/PackFlashItemImages/WebReady/future-oil-and-gas-opportunities-for-women-and-minorities-2014-04apr-16-hero.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 12894 Energy Policy Blog

See Also: Field Seminar

This field seminar offers an excellent opportunity for the students to walk on a variety of modern terrigenous clastic depositional systems while observing sedimentary processes, modern sedimentary structures, and numerous trenches illuminating the three-dimensional architecture of each area.

Desktop /Portals/0/PackFlashItemImages/WebReady/fs-Modern-Terrigenous-Clastic-Depositional-Systems.jpg?width=50&h=50&mode=crop&anchor=middlecenter&quality=90amp;encoder=freeimage&progressive=true 13368 Field Seminar